[R-sig-Geo] Best way to calculate distance between geographicalpoints

[Roger Bivand]

On Thu, 14 Jan 2010, ONKELINX, Thierry wrote:

> Dear Karl,
>
> I think that the relative errors are more relevant than absolute errors.
> The relative error on the equatorial circumference for "geo.dist" is
> 0.33%, which is not that accurate. The relative error on the meridional
> distance is only about 0.085%, which should accurant enough for most
> applications.

>From the code of rdist.earth(), it is using a sphere with a 6378388m 
parameter (which is like the International 1909 ellipsoid, but a sphere). 
geod.dist() is using WGS84 a=6378137.0  rf=298.257223563:

http://code.google.com/p/r-oce/source/browse/trunk/R/misc.R

near line 280. The code under spDistsN1() uses WGS84 values, but with the 
radius in km:

http://r-spatial.cvs.sourceforge.net/viewvc/r-spatial/sp/src/gcdist.c?revision=1.6&view=markup

So in principle geod.dist() and spDistsN1(..., longlat=TRUE) should yield 
equivalent results, because their assumptions are the same.

Several of the references suggest that the geographic pole should not be 
input. It looks as though the oce implementation handles this more 
gracefully than sp.

Hope this helps,

Roger

>
> Just my 2 eurocents.
>
> Thierry
>
>
> ------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek
> team Biometrie & Kwaliteitszorg
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> Research Institute for Nature and Forest
> team Biometrics & Quality Assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
>
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be
> www.inbo.be
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to
> say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of
> data.
> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: r-sig-geo-bounces at stat.math.ethz.ch
> [mailto:r-sig-geo-bounces at stat.math.ethz.ch] Namens Karl Ove Hufthammer
> Verzonden: donderdag 14 januari 2010 10:57
> Aan: r-sig-geo at stat.math.ethz.ch
> Onderwerp: Re: [R-sig-Geo] Best way to calculate distance between
> geographicalpoints
>
> On Thu, 14 Jan 2010 10:27:17 +0100 Karl Ove Hufthammer <karl at huftis.org>
> wrote:
>> I have found three functions for calculating the distance between
>> geographical points, 'geo.dist' in the 'oce' package, 'rdist.earth' in
>
>> the 'fields' package, and 'spDistsN1' in the 'sp' package. They all
>> give slightly difference answers, so my question is: which of them is
>> best, i.e., gives the most accurate answer?
>
> One simple test would be to calculate the circumference of the earth at
> the equator and the meridian. But this test gives conflicting answers.
>
> According to Wikipedia, "http://en.wikipedia.org/wiki/Earth" the
> equatorial circumference is 40075.02 km and the meridional circumference
> is 40007.86 km.
>
> When calculating half the equatorial circumference, 'spDistsN1' is best,
> and gives the *exact* answer, while 'rdist.earth' is close (less than
> one km difference), and 'geo.dist' is far from the correct answer
> (133.92 km difference). So it would initially seem that 'spDistsN1' is
> the one to use, and one should avoid 'geo.dist'.
>
> But when calculating the meridional distance, 'geo.dist' gives the exact
> answer, while both 'rdist.earth' and 'spDistsN1' are both off by about
> 34 km (but in difference directions).
>
> So which to use is still an open question ...
>
> Here is the code I used:
>
> library(oce)
> library(fields)
> library(sp)
>
> # Equatorial
> lt1=0
> lt2=0
> lg1=0
> lg2=180
>
> a=matrix(c(lg1,lt1),nrow=1)
> b=matrix(c(lg2,lt2),nrow=1)
>
> # Calculated distance
> geod.dist(lt1,lg1,lt2,lg2)
> rdist.earth(a,b, miles=FALSE)
> spDistsN1(a,b, longlat=TRUE)
>
> # Correct distance (according to Wikipedia)
> 40075.02/2
>
>
> # Meridional
> lt1=-90
> lt2=90
> lg1=0
> lg2=0
>
> a=matrix(c(lg1,lt1),nrow=1)
> b=matrix(c(lg2,lt2),nrow=1)
>
> # Calculated distance
> geod.dist(lt1,lg1,lt2,lg2)
> rdist.earth(a,b, miles=FALSE)
> spDistsN1(a,b, longlat=TRUE)
>
> # Correct distance (according to Wikipedia)
> 40007.86/2
>
> --
> Karl Ove Hufthammer
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
> Druk dit bericht a.u.b. niet onnodig af.
> Please do not print this message unnecessarily.
>
> Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer
> en binden het INBO onder geen enkel beding, zolang dit bericht niet bevestigd is
> door een geldig ondertekend document. The views expressed in  this message
> and any annex are purely those of the writer and may not be regarded as stating
> an official position of INBO, as long as the message is not confirmed by a duly
> signed document.
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no